   Chapter 9.3, Problem 9E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Let f ( x ) = 3 x 2 − 2 x .(a) Use the definition of derivative and the Procedure/Example box on page 562 to verify that f ' ( x ) = 6 x − 2 .(b) Find the instantaneous rate of change of .(c) Find the slope of the tangent to the graph of y = f ( x )  at  x =   − 1 .(d) Find the point on the graph of y = f ( x )  at  x =   − 1 .

(a)

To determine

To prove: The derivative of function f(x) is f'(x)=6x2 if f(x)=3x22x.

Explanation

Given Information:

The function f(x) is f(x)=3x22x and f'(x)=6x2.

Formula used:

If a function f(x) is defined in the interval [x+h,x], then its derivative is given by the formula,

f'(x)=limh0f(x+h)f(x)h

Proof:

Consider the provided statement,

The function f(x) is f(x)=3x2+2x+11 and f'(x)=6x+2.

Substitute x=x+h in f(x) to get,

f(x+h)=3(x+h)2+2(x+h)+11f(x+h)=3(x2+h2

(b)

To determine

To calculate: The instantaneous rate of change of function f(x) at x=1 if f(x)=3x22x and f'(x)=6x2.

(c)

To determine

To calculate: The slope to the tangent of the graph y=f(x) at x=1 if f(x)=3x22x and f'(x)=6x2.

(d)

To determine

The point on the graph of y=f(x) at x=1 if f(x)=3x22x and f'(x)=6x2.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 